# University of Twente Student Theses

## Testing the standard DNB model for calculation of solvency buffers for pension funds: statistical argumentation for change to internal models and guideline for (partial) internal models

Lent, J. van
(2013)
*Testing the standard DNB model for calculation of solvency buffers for pension funds: statistical argumentation for change to internal models and guideline for (partial) internal models.*

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Abstract: | To be able to meet their future obligations pension funds are required to have solvency buffers, which are designed to account for the risks pension funds are associated with. These required equity buffers (Vereist Eigen Vermogen, VEV) are determined by a standard model proposed by the Dutch regulator (DNB), which gives a certainty of 97.5% that a pension fund is able to meet its obligations over a period of one year. The DNB model is based on certain scenarios that can happen in one year time and are based on predetermined parameters. This model will be revised in 2015. Research goal and main research question Pension funds that have risks that are not covered by the standard model have the option to change to a (partial) internal model to measure the required amount of equity. This report gives statistical argumentation for the change to internal models. This is done by comparing the DNB model with a historical 97.5% Value-at-risk (VaR) model. This research gives an answer to the following main research question: Is the DNB model for calculation of VEV sufficient compared with a historical 97.5% VaR model or to which extension should it be replaced by a partial internal model? Research method In this research six synthetic (virtual) pension funds and the average pension fund in the Netherlands are used as input to test the DNB models. Every synthetic pension fund has its risk profile based on the asset mix of the pension fund and the interest hedge ratio, which are the main factors that determine the risk pension funds have. The values of VEV per pension fund as result of the current DNB model and the model in 2015 are tested in two ways. First the models are compared with a 97.5% Value-at-Risk (VaR) model based on historical simulation. With this model 415 expected future values of a portfolio of a pension fund are estimated using 415 10-day returns of market variables from a historical period (years 1997 till 2013). These 10-day returns are transformed into yearly profits and losses. The 10th worst simulated future loss is the amount of VEV that corresponds with a 97.5% confidence level of the VaR model, which is compared with results of VEV of the DNB model. Besides the comparison with the 97.5% VaR model individual risk factors of the DNB models are back-tested against historical movements of market variables to see if the models give a good estimation of the risk associated with these variables. The DNB models are rejected (indicated by the color red in columns VEV DNB model in Table of results) if the value of VEV is not in the non-rejection region of the 97.5% VaR model. This non-rejection region is based on Kupiec’s test, which is a statistical test that determines whether an observed frequency of exceptions is consistent with the number of expected exceptions according to the 97.5% VaR model. An exception occurs when the simulated loss is less than the 97.5% VaR confidence level. The non-rejection region is a confidence interval of the number of exceptions that are acceptable based on the Kupiec’s test statistic, which is the critical value of a chi-square distribution with one degree of freedom and a confidence level of 97.5%. The lower boundary of the non-rejection region is the 19th worst simulated loss of the 97.5% VaR model and the higher boundary is the 5th worst simulated loss. This leads to the following null-hypothesis and alternative hypothesis: : Value of VEV DNB model is in non-rejection region of the 97.5% VaR model Value of VEV DNB model is outside non-rejection region of 97.5% VaR model If the null-hypothesis is rejected the DNB model is rejected by Kupiec’s test. Results The results show that for pension funds with low hedge ratios the value of VEV as result of the current DNB model is outside the non-rejection region and therefore the null-hypothesis is rejected. Comparing pension funds with the same asset mix, the pension fund with the lower hedge ratio (funds 1, 3, 5) is rejected, while the fund with the higher hedge ratio (pension funds 2, 4 and 6) is not rejected. This is because there is a significant difference between the amount of interest rate risk in the DNB models and the 97.5% VaR model, especially for pension funds with low hedge ratios. Based on the rejection of the DNB model for pension funds with low interest hedge ratios (pension funds 1, 3 and 5) the DNB model seems to underestimate interest rate risk. Results of the DNB model are based on the assumption that the returns of interest rates used to calculate the present value of fixed assets (bonds, interest rate swaps, forwards) and liabilities (future retirement obligations) are distributed normally. Back-tests of the returns of euro swap rates in years 1997-2013 show that these returns do not follow a normal distribution, especially for assets and liabilities with short term maturities (1-10 years). Besides that the interest rates in the historical back-test period have higher volatility than expected by the DNB model, this leads to a large difference of required equity for interest rate risk between the historical 97.5% VaR model and the DNB models. Back-tests show that the scenarios for credit risk of the DNB model in 2015 overestimate credit risk especially for AAA rated assets. For pension fund six, with a large amount of fixed assets with credit rating AAA, the rejection of the DNB model in 2015 is a consequence of this overestimation of credit risk. |

Item Type: | Essay (Master) |

Faculty: | BMS: Behavioural, Management and Social Sciences |

Subject: | 85 business administration, organizational science |

Programme: | Business Administration MSc (60644) |

Link to this item: | http://purl.utwente.nl/essays/63844 |

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